integration (1 Viewer)

[ashokkumar]

integrate cosx/(sinx)^2

 

[The Nomad]

Cos x/(Sin x)^2 = Cosec x Cot x.

Integration(Cosec x Cot x) = - Cosec x.

 

[ashokkumar]

Cos x/(Sin x)^2 = Cosec x Cot x.

Integration(Cosec x Cot x) = - Cosec x.

How'd you know the integral of (Cosec x Cot x) = - Cosec x? Is that just a general rule? (It isn't on the standard integrals )

 

[kaz1]

Dude reverse chain rule S[f'(x)*f(x)ⁿ]= f(x)ⁿ⁺¹/n+1

 

[ashokkumar]

reverse chain rule what?

 

[shaon0]

reverse chain rule what?

Let u=sin(x): du=cos(x) dx
I=S cos(x)/(sin(x))^2 dx
=S du/u^2
=-1/u +C
=-cosec(x)+C

 

[kaz1]

reverse chain rule what?

learn your mafs! look in a 2unit textbook.

 

[Trebla]

Have you learnt how to integrate trigonometric functions in Ext1 yet?

 

[The Nomad]

How'd you know the integral of (Cosec x Cot x) = - Cosec x? Is that just a general rule? (It isn't on the standard integrals )

Differentiation of Sec x = Sec x Tan x.
Differentiation of Cosec x = - Cosec x Cot x.

 

[Nahidul]

reverse chain rule what?

Basically what the 'reverse' chain rule states is :

Thus for this example:
( csc x = cosec x )
This rule can be very helpful in Ext. 1 and Ext. 2.

 

[gurmies]

Basically what the 'reverse' chain rule states is :

Thus for this example:
( csc x = cosec x )
This rule can be very helpful in Ext. 1 and Ext. 2.

You shouldn't write your cosecs that way. Too easily mistaken with arcsin.

 

[Nahidul]

which way shouldnt i write cosecs? if you mean the 'csc' then i cant help that because thats how the function is loaded in the latex equation editor.

 

[Aquawhite]

I keep forgetting this rule in exam situations and only remembering it at the last minutes of the exam and then missing out on fully completing such a simple question. And I love the integration sections too

 

[Carrotsticks]

You shouldn't write your cosecs that way. Too easily mistaken with arcsin.

Everywhere else in the world uses csc for Cosec. It is only the NSW syllabus which uses Cosec, which is kinda crap. (Much like they use -mCAT for chemistry)

Think about it, all the trigonometric functions are 3 letters. Sin, Cos, Tan, Sec, then suddenly Cosec?

I understand that it may look similar to arcsin, but that's more of the reader's problem.

 

[Drongoski]

Having to use 'cosec' is stupid.

 

[untouchablecuz]

which way shouldnt i write cosecs? if you mean the 'csc' then i cant help that because thats how the function is loaded in the latex equation editor.

what he meant was if you write csc x = sin^-1x it can be mistaken as arcsin which is generally written as sin^-1x

i.e csc x = sin^-1x can be mistaken to mean csc x = arcsin x

 

[Carrotsticks]

what he meant was if you write csc x = sin^-1x it can be mistaken as arcsin which is generally written as sin^-1x

i.e csc x = sin^-1x can be mistaken to mean csc x = arcsin x

Yes the confusion between inverse trig with powers is stupid.

For example, if you want to show f(x) squared, it can be typed as



But if you want to show 1/f(x), it implies it can also be typed up as



which is the same as inverse functions.

This is much like how inverse sinx is shown as



which is technically the same as 1/sinx in terms of transcription.

To avoid the confusion, I guess just actually use Arcsin, though unorthodox. Also you can use actual fractions when showing 1/sinx rather than

Other than that, I see no reason why people would automatically make the association between csc and arcsin.

 

[adomad]

or u can do it this way:







noobish i know but its just another way.

 

[Gussy Booo]

integrate: cosx/sinx^2 dx


d/dx sinx = cosx
therefore dsinx = cosxdx
so we are now integrating

(1/sinx^2)d(sinx) ---> in respect to sinx.

and so:
=sinx^-2 d(sinx)
=(-1)sinx^-1
=-cosecx+c

i love integration. you have to be flexible <3

 

[Drongoski]

integrate: cosx/sinx^2 dx


d/dx sinx = cosx
therefore dsinx = cosxdx
so we are now integrating

(1/sinx^2)d(sinx) ---> in respect to sinx.

and so:
=sinx^-2 d(sinx)
=(-1)sinx^-1
=-cosecx+c

i love integration. you have to be flexible <3

That's the way to do it. By the way it's "with respect to sin x"